Nearly half the groups that bought po­lit­i­cal ads on Face­book dur­ing the fi­nal, cru­cial weeks of the 2016 elec­tion sea­son were black holes with lit­tle, if any, in­for­ma­tion avail­able to in­di­cate who they were or where their fi­nan­cial back­ing came from, re­searchers said Mon­day.

In a new study that de­tails the ef­fort to in­flu­ence Amer­i­can elec­tions via so­cial me­dia, Univer­sity of Wis­con­sin-Madi­son an­a­lysts re­ported that of the 228 groups that bought ads on sen­si­tive po­lit­i­cal is­sues such as gun con­trol and il­le­gal im­mi­gra­tion, 122 were deemed “sus­pi­cious.” The def­i­ni­tion of “sus­pi­cious,” the re­searchers said, is that there was vir­tu­ally no pub­licly avail­able in­for­ma­tion about them.

Of those 122, it’s be­lieved that about 20 had clear, di­rect links to the Krem­lin, an­a­lysts said af­ter cross-ref­er­enc­ing their find­ings with House In­tel­li­gence Com­mit­tee in­for­ma­tion.

The shad­owy or­ga­ni­za­tions — which were able to shield their iden­ti­ties and fund­ing sources be­cause they op­er­ate on­line, un­like those that ad­ver­tised on more tra­di­tional medi­ums such as tele­vi­sion or ra­dio — tar­geted vot­ers in key swing states such as Penn­syl­va­nia and Wis­con­sin, us­ing emo­tion­ally charged ads tai­lored to fit the de­mo­graph­ics and spe­cific po­lit­i­cal con­cerns of the vot­ing blocs in those ar­eas.

The new data come just days af­ter Face­book founder and CEO Mark Zucker­berg tes­ti­fied be­fore Congress for nearly 10 hours, answering law­mak­ers’ ques­tions on how the so­cial me­dia giant would bet­ter pro­tect users’ data and en­sure mys­te­ri­ous groups could no longer buy ads on the site with­out ac­count­abil­ity. He voiced sup­port for steps that would re­quire on­line ad-buy­ers to dis­close their iden­ti­ties and fund­ing, some­thing crit­ics say is des­per­ately needed to en­sure his­tory doesn’t re­peat it­self dur­ing the up­com­ing 2018 midterms.

“This se­crecy would not be pos­si­ble on broad­cast ad­ver­tis­ing,” said Univer­sity of Wis­con­sin pro­fes­sor Young Mie Kim, the lead re­searcher on the study who ex­am­ined about 5 mil­lion paid ads shown on Face­book be­tween Sept. 28 and Elec­tion Day on Nov. 8.

“Any TV or ra­dio ad that per­tains to a ‘po­lit­i­cal mat­ter of na­tional im­por­tance’ is sub­ject to ba­sic lev­els of trans­parency: broad­cast­ers must col­lect in­for­ma­tion about the group that bought the ad­ver­tise­ment, as well as how much the group paid for the ad and where it was dis­sem­i­nated,” she con­tin­ued.

In her re­view, Ms. Kim calls on Congress to pass the Hon­est Ads Act, bi­par­ti­san leg­is­la­tion that would bar some anony­mous po­lit­i­cal ad­ver­tis­ing on so­cial me­dia sites. The study was re­leased in con­junc­tion with the Cam­paign Le­gal Cen­ter and Is­sue One, two ad­vo­cacy groups that also are ex­plic­itly push­ing the Hon­est Ads Act.

Mr. Zucker­berg ex­plic­itly en­dorsed the leg­is­la­tion dur­ing his con­gres­sional tes­ti­mony last week, cast­ing it as part of a broader move to reg­u­late the so­cial me­dia gi­ants that now shape Amer­ica’s cul­tural and po­lit­i­cal land­scape but lack the gov­ern­ment over­sight of vir­tu­ally ev­ery other in­dus­try.

“The in­ter­net is grow­ing in im­por­tance around the world in peo­ple’s lives; I think it’s in­evitable that there will be some reg­u­la­tion,” Mr. Zucker­berg told Congress dur­ing his marathon tes­ti­mony last week.

The Hon­est Ads Act has at least some bi­par­ti­san sup­port; it was in­tro­duced by Demo­cratic Sens. Amy Klobuchar of Min­ne­sota and Mark Warner of Vir­ginia, along with Repub­li­can Sen. John Mc­Cain of Ari­zona.

Mr. Mc­Cain has called on fel­low law­mak­ers to ad­dress the “loop­holes” that al­low in­ter­net ad-buy­ers to es­cape vir­tu­ally any re­port­ing re­quire­ments.

Had they been in place in 2016, such laws would’ve shed at least a lit­tle bit of light on ex­actly how tar­geted and pre­cise the Face­book ad­ver­tis­ing cam­paign truly was.

Ac­cord­ing to Ms. Kim’s re­search, the ads from “sus­pi­cious” sources fol­lowed the tra­di­tional po­lit­i­cal play­book of di­rect­ing most of their fire at key bat­tle­ground states, and high­light­ing hot-but­ton is­sues that were es­pe­cially im­por­tant to vot­ers there.

For ex­am­ple, vot­ers in Wis­con­sin saw ads re­lated to a host of con­tro­ver­sial is­sues such as guns, im­mi­gra­tion, ter­ror­ism, and racial con­flict, while vot­ers in Michi­gan were “dis­pro­por­tion­ally tar­geted” with ads about ter­ror­ism and na­tional se­cu­rity.

Low-in­come vot­ers were shown more ads about im­mi­gra­tion and race is­sues than wealth­ier vot­ers, the data show.

While the Hon­est Ads Act is cer­tainly no sil­ver bul­let — the study con­cedes that just 38 per­cent of the ads in ques­tion would’ve been forced to dis­close their fund­ing under the bill — it seems to be some­thing of a start­ing point for law­mak­ers and Sil­i­con Val­ley, with both sides fac­ing pub­lic pres­sure to clamp down on for­eign in­ter­fer­ence.

Last week, on the heels of Mr. Zucker­berg’s tes­ti­mony, Twit­ter said it will con­tinue work on its own vol­un­tary “Ads Trans­parency Cen­ter,” a new plat­form aimed at ed­u­cat­ing vot­ers about where po­lit­i­cal ads come from.

The pro­gram “will dra­mat­i­cally in­crease trans­parency for po­lit­i­cal and is­sue ads, pro­vid­ing peo­ple with sig­nif­i­cant de­tail on the ori­gin of each ad,” the com­pany said, adding it plans to launch the cen­ter this sum­mer.